Show that the bisectors of angles of a parallelogram form a rectangle.
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To prove: MNOP is a rectangle.
In parallelogram ABCD
∠A=∠D=90⁰
[they form a straight line]
∴IN△AMD,∠M=90⁰
∠M=∠N=90⁰
[they form a straight line]
Similarly,
∠M=∠P=90⁰
And
∠P=∠O=90⁰
∴∠MPO=∠PON∠ONM=∠NMO=90⁰
∴ MNOP is a rectangle. [A rectangle is a parallelogram with one angle 90⁰]
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Answer:
ANSWER
To prove: MNOP is a rectangle.
In parallelogram ABCD
∠A=∠D=90
∘
[they form a straight line]
∴IN△AMD,∠M=90
∘
∠M=∠N=90
∘
[they form a straight line]
Similarly,
∠M=∠P=90
∘
And
∠P=∠O=90
∘
∴∠MPO=∠PON∠ONM=∠NMO=90
∘
∴ MNOP is a rectangle. [A rectangle is a parallelogram with one angle 90
∘
]
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